Question Number 198419 by Nimnim111118 last updated on 19/Oct/23
$$\:\:{Please}\:{Help}... \\ $$$$\:\:\int\underset{{S}} {\int}{x}^{\mathrm{2}} {dydz}+{y}^{\mathrm{2}} {dzdx}+\mathrm{2}{z}\left({xy}−{x}−{y}\right){dxdy}\:{where} \\ $$$$\:\:\:{S}\:{is}\:{the}\:{surface}\:{of}\:{the}\:{cube}.\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1},\:\mathrm{0}\leqslant{y}\leqslant\mathrm{1}, \\ $$$$\:\:\:\:\mathrm{0}\leqslant{z}\leqslant\mathrm{1} \\ $$$$ \\ $$